Root cause discovery via permutations and Cholesky decomposition

TL;DR

This paper introduces a novel method for root cause discovery in linear structural models using permutations and Cholesky decomposition, enabling identification of disease-causing genes from observational and interventional data.

Contribution

It provides a new identifiability proof for root cause discovery without assuming causal order, and proposes a permutation-based method applicable to high-dimensional data.

Findings

The method successfully identifies root causes in simulations.

It accurately discovers disease-causing genes in real gene expression data.

The approach is effective even in high-dimensional settings.

Abstract

This work is motivated by the following problem: Can we identify the disease-causing gene in a patient affected by a monogenic disorder? This problem is an instance of root cause discovery. In particular, we aim to identify the intervened variable in one interventional sample using a set of observational samples as reference. We consider a linear structural equation model where the causal ordering is unknown. We begin by examining a simple method that uses squared z-scores and characterize the conditions under which this method succeeds and fails, showing that it generally cannot identify the root cause. We then prove, without additional assumptions, that the root cause is identifiable even if the causal ordering is not. Two key ingredients of this identifiability result are the use of permutations and the Cholesky decomposition, which allow us to exploit an invariant property across different permutations to discover the root cause. Furthermore, we characterize permutations that yield the correct root cause and, based on this, propose a valid method for root cause discovery. We also adapt this approach to high-dimensional settings. Finally, we evaluate the performance of our methods through simulations and apply the high-dimensional method to discover disease-causing genes in the gene expression dataset that motivates this work.